Immersed electrokinetic finite element method, computer methods in. A new edition of the leading textbook on the finite element method, incorporating major advancements and further applications in the field of electromagnetics the finite element method fem is a powerful simulation technique used to solve boundaryvalue problems in a variety of engineering circumstances. This paper summarizes the newly developed immersed finite element method ifem and its applications to the modeling of biological systems. Sheldon wang 2 and others 1 department of mechanical engineering northwestern university evanston, il 60208 2 department of mathematical sciences new jersey institute of technology newark, nj 07102. The finite element method for the analysis of nonlinear and dynamic systems prof. The proposed immersed molecular electrokinetic finite element method couples electrokinetics with fluctuating hydrodynamics to study the. The finite element methods notes pdf fem notes pdf book starts with the topics covering introduction to finite element method, element shapes, finite element analysis pea, fea beam elements, fea two dimessional problem, lagrangian serenalipity elements, isoparametric formulation, numerical integration, etc. Kafafy abstract a new particleincell algorithm was developed for plasma simulations involving complex boundary conditions.
The weak formulation wf may be computed numerically by an implicit algorithm with the finite element method, and the streamline upwindpetrovgalerkin method. Optimal approximation errors in l 2 norm and h 1 semi. In the finite difference setting, we refer to the immersed boundary method in. Daryl logan, a first course in finite element method, thomson, india edition. Liu contributed chapter 12 entitled immersed meshfree finite element method and applications 7. Finite element modeling of electromagnetic systems mathematical and numerical tools unit of applied and computational electromagnetics ace dept. A partially penalized p1cr immersed finite element method. Nanoparticle translocation through conical nanopores. Immersed finite element method for interface problems with. The 3d immersed molecular electrokinetic finite element method imefem will be presented for the modeling of micro fluidic electrokinetic assembly of nanowires, filaments and biomolecules. Kopacz, a woonhong yeo, b jaehyun chung c and wing kam liu ad. The extended finite element method xfem is a numerical technique based on the generalized finite element method gfem and the partition of unity method pum. Request pdf immersed molecular electrokinetic finite element method for nanodevices in biotechnology and gene delivery it has been demonstrated from recent research that modern uses of. The new algorithm is based on the threedimensional immersed.
The method presented here uses immersed finite element ife functions for the discretization in spatial variables that can be carried out over a fixed mesh such as a cartesian mesh if desired, and this feature makes it possible to reduce the parabolic equation to a system of ordinary differential equations ode through the usual semi. Immersed electrokinetic finite element method 381 here, the immersed. We thus remain in the regime, for which previous studies have shown the electrokinetic equa. Design and optimization of a nanotip sensor via immersed molecular electrokinetic finite element method. As such, it is a numerical rather than an analytical method. Abstract a new method is proposed for modelling the electrokinetic. A consistent immersed finite element method for the interface. A hermite cubic immersed finite element space for beam designs tzin s. An immersed smoothed finite element method for fluidstructure interaction problems. Department of engineering, university of cambridge, uk summary we propose a robust immersed. It has been widely used for analysis of electromagnetic fields in antennas, radar. Computer methods in applied mechanics and engineering. This transformative bionanotechnology is being developed to enable drug delivery.
Design and optimization of a nanotip sensor via immersed. One is the extended finite element method xfem and the other is the immersed finite element method ifem. The proposed immersed molecular electrokinetic finite element method couples electrokinetics with fluctuating hydrodynamics to study the motion and deformation of flexible objects immersed in a. In the early 1960s, engineers used the method for approximate solutions of problems. Keywords finite difference method, finite element method, fluidstructure interaction, immersed boundary method. Immersed finite element particleincell simulations of ion propulsion raed i. This work was inspired by the pioneering work of professor t. Eleni chatzi lecture 3 october, 2014 institute of structural engineering method of finite elements ii 1.
Jun 27, 2012 read nanoscale sensor analysis using the immersed molecular electrokinetic finite element method, nanoscale on deepdyve, the largest online rental service for scholarly research with thousands of academic publications available at your fingertips. Mathematical foundations of the immersed finite element method. Bilinear immersed finite elements for interface problems. There are two classes of methods which belong to this type. Finite element methods for the numerical solution of partial differential equations vassilios a. Immersed finite element method and its applications to biological. Finite element methods pdf notes fem pdf notes smartzworld. The interfaces do not have to be one of grid points. In this paper, the immersed finite element method ifem is proposed for the solution of complex fluid and deformable structure interaction problems encountered in many physical models.
In ifem, a lagrangian solid mesh moves on top of a background eulerian fluid mesh which spans over the entire computational domain. However, our framework described here can be used for high order immersed interface. Immersed electrokinetic finite element method y liu, wk liu, t belytschko, n patankar, ac to, a kopacz, jh chung international journal for numerical methods in engineering 71 4, 379405, 2007. Multiscale framework for biomedical simulation from.
Theory, implementation, and practice november 9, 2010 springer. Immersed finite element particleincell simulations of. A 3d immersed finite element method with nonhomogeneous interface flux jump for applications in particleincell simulations of plasmalunar surface. Immersed finite element method and its applications to. The immersed interface method using a finite element. The method uses the immersed boundaryelement method and the smoothed finite element method and hence it is termed as isfem. Proceedings of the asme 2010 first global congress on nanoengineering for medicine and biology.
Bilinear immersed finite elements for interface problems xiaoming he abstract in this dissertation we discuss bilinear immersed. Highorder extended finite element methods for solving. A new method is proposed for modelling the electrokineticinduced mechanical motion of particles in a fluid domain under an applied electric field. Immersed finite element method northwestern scholars. Hughes in solving fluidstructure interaction problems. The method uses the immersed boundary element method and the smoothed finite element method and hence it is termed as isfem.
A finite element method is proposed for one dimensional interface problems involving discontinuities in the coefficients of the differential equations and the derivatives of the solutions. Highorder extended finite element methods for solving interface problems. Immersed finite element method for fluidstructure interactions. Multiscale framework for biomedical simulation from molecular. A hermite cubic immersed finite element space for beam. This ife space is based upon meshes that can be independent of interface of the materials used to form a beam. For simplicity, a piecewise constant function is applied here, which is assumed to be constant within c and vanish somewhere else, as given.
The related research works can be categorized into three aspects. The early success of immersed finite element formulations for the immersed methods is only the beginning of this type of modeling treatment for complex fsi systems. Immersed electrokinetic finite element method lehigh university. The isfem is a partitioned approach and does not need a bodyfitted mesh for fsi simulations.
The proposed immersed molecular electrokinetic finite element method couples electrokinetics with fluctuating hydrodynamics to study the motion and deformation of flexible objects immersed in a suspending medium under an applied electric field. Linear finite element methods the nite element methods provide spaces vnof functions that are piecewise smooth and \simple, and locally supported basis function of these spaces to achieve good approximations of the solution u2v, an e cient assembly of the system matrix with desirable properties e. Pdf available in international journal of computational methods 84. In this paper, we solve the electrokinetic equations numerically via the nite element method, to investigate the problem of current and ow recti cation in a conical nanopore, as well as the translocation of a nanoparticle though such a pore. We propose a partially penalized p 1 cr immersed finite element ife method with midpoint values on edges as degrees of freedom for cr elements to solve planar elasticity interface problems. An introduction to the finite element method second edition j. Immersed finite element method and its applications to biological systems wing kam liu 1, yaling liu, david farrell, lucy zhang1, x. Asme 2010 first global congress on nanoengineering for medicine and biology. In the xfem, they use enrichment basis functions in addition to the standard finite element basis. Compared with the successful immersed boundary method ibm by peskin and coworkers j comput phys 160.
Pdf an immersed smoothed finite element method for fluid. Jun 20, 2007 immersed electrokinetic finite element method yaling liu department of mechanical engineering, northwestern university, 2145 sheridan road, evanston, il 60208. These are the direct approach, which is the simplest method for solving discrete problems in 1 and 2 dimensions. Immersed finite element methods for elliptic interface problems with nonhomogeneous jump conditions xiaoming he, tao lin, and yanping lin abstract. Basedon the ife method, the immersed finite element particleincell. Intermsofhatbasisfunctionsthismeansthatabasisforvh. Liu y, liu wk, belytschko t, patankar na, to ac, kopacz a, chung jh, immersed electrokinetic finite element method, international journal for numerical methods in engineering 71 4. On computational issues of immersed finite element methods. The finite element method in electromagnetics, 3rd edition. Pe281 finite element method course notes summarized by tara laforce stanford, ca 23rd may 2006 1 derivation of the method in order to derive the fundamental concepts of fem we will start by looking. Hybrid finite differencefinite element immersed boundary.
Oct 16, 2012 the proposed immersed molecular electrokinetic finite element method couples electrokinetics with fluctuating hydrodynamics to study the motion and deformation of flexible objects immersed in a suspending medium under an applied electric field. Immersed finite element method for interface problems with algebraic multigrid solver by wenqiang feng a thesis presented to the faculty of the graduate school of missouri university of science and technology in partial ful. This transformative bionanotechnology is being developed to enable gene delivery systems to achieve desired therapeutic effects and for the design and. Therefore, it is suitable for moving interface problems. Immersed molecular electrokinetic finite element method.
Taylor, the finite element method, vols 1 and 2, butterworth heinemann, 2000 klausjurgen bathe, finite element procedures part 12, prentice hall, 1995. Immersed and discontinuous finite element methods nabil chaabane abstract in this dissertation we prove the superconvergence of the minimaldissipation local discontinuous galerkin method for elliptic problems and construct optimal immersed nite element approximations and discontinuous immersed nite element methods for the stokes interface. The 3d immersed molecular electrokinetic finite element method imefem will be presented for the modeling of micro fluidic electrokinetic assembly of nano wires and filaments and biomolecules. We present a high performance modularlybuilt opensource software openifem. Immersed electrokinetic finite element method request pdf. It is used mainly for problems for which no exact solution, expressible in some mathematical form, is available. It extends the classical finite element method by enriching the solution space for solutions to differential equations with. Request pdf immersed finite element method for fluidstructure interactions in this paper, we present a detailed derivation of the numerical method, immersed. Request pdf immersed electrokinetic finite element method a new method is proposed for modelling the electrokineticinduced mechanical motion of particles in a fluid domain under an applied. Nanoscale sensor analysis using the immersed molecular electrokinetic finite element method adrian m. The immersed molecular electrokinetic finite element method imefem framework used in our study is an extension of our previous verified and validated. This work also contrasts two different weak forms of the equations, one of which is demonstrated to be more effective for the coarse structural discretizations facilitated by our coupling approach.
In this method, independent solid meshes move in a fixed background field mesh that models the fluid and the electric field. Nanoscale sensor analysis using the immersed molecular. Immersed interface finiteelement methods 475 triangular immersed interface. Immersed finite element method for rigid body motions in. Introduction to the finite element method fem lecture 1 the. Advances immersed molecular electrokinetic in computational. More recently, inspired by ib method, the immersed finite element method ifem, the immersed continuum method icm, and the extended immersed boundary method eibm were developed to solve the motion and large deformation of incompressible hyperelastic material within an incompressible or slightly compressible fluid. A novel method called immersed smoothed fem using three.
The finite element method for electromagnetic modeling. Na an, xijun yu, huanzhen chen, chaobao huang and zhongyan liu, a partially penalty immersed crouzeixraviart finite element method for interface problems, journal of inequalities and applications, 2017, 1, 2017. Furthermore, ifem is combined with electrokinetics to study the mechanisms of nanobio filament assembly for the understanding of cell motility. Dougalis department of mathematics, university of athens, greece and institute of applied and computational mathematics, forth, greece revised edition 20. Fundamentals of the method as well as new advances in the field are described in detail. N2 in this paper, the immersed finite element method ifem is proposed for the solution of complex fluid and deformable structure interaction problems encountered in many physical models. Louis san francisco auckland bogota caracas lisbon london madrid mexico milan montreal new delhi paris san juan singapore sydney tokyo toronto. In these earlier finite element based immersed methods, explicit time inte. A method of lines based on immersed finite elements for.
Recent mathematical studies and extensions to electrokinetics and mass and heat transfers can also be found in refs. Datta s, ghosal s, patankar na, electroosmotic flow in a rectangular channel with variable. An immersed finite element method with integral equation. Finite element analysis is a method of solving, usually approximately, certain problems in engineering and science. An immersed finite element method with integral equation correction thomas ruberg and fehmi cirak. Immersed electrokinetic finite element method liu 2007. Partially penalized immersed finite element methods for. Read nanoscale sensor analysis using the immersed molecular electrokinetic finite element method, nanoscale on deepdyve, the largest online rental service for scholarly research with thousands of academic publications available at your fingertips. The finite element method for the analysis of nonlinear and.